MinT - Best Known (98−71, 98, s)-Nets in Base 27

Best Known (98−71, 98, s)-Nets in Base 27

(98−71, 98, 114)-Net over F₂₇ — Constructive and digital

Digital (27, 98, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 98, 114)-net over F₂₇, using
- net from sequence [i] based on digital (23, 113)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 23 and N(F) ≥ 114, using
    - an explicitly constructive algebraic function field [i]

(98−71, 98, 116)-Net in Base 27 — Constructive

(27, 98, 116)-net in base 27, using

2 times m-reduction [i] based on (27, 100, 116)-net in base 27, using
- base change [i] based on digital (2, 75, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(98−71, 98, 208)-Net over F₂₇ — Digital

Digital (27, 98, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 98, 208)-net over F₂₇, using
- net from sequence [i] based on digital (24, 207)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 24 and N(F) ≥ 208, using
    - an algebraic function field by Beelen and Pellikaan [i]

(98−71, 98, 4938)-Net in Base 27 — Upper bound on s

There is no (27, 98, 4939)-net in base 27, because

1 times m-reduction [i] would yield (27, 97, 4939)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 6 974481 136251 484281 789298 922517 584461 939054 371606 957406 773429 966105 050771 214722 965764 555277 192337 542703 667127 254447 138040 521622 796650 045347 > 27⁹⁷ [i]