MinT - Best Known (98−69, 98, s)-Nets in Base 27

Best Known (98−69, 98, s)-Nets in Base 27

(98−69, 98, 114)-Net over F₂₇ — Constructive and digital

Digital (29, 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]

(98−69, 98, 150)-Net in Base 27 — Constructive

(29, 98, 150)-net in base 27, using

2 times m-reduction [i] based on (29, 100, 150)-net in base 27, using
- base change [i] based on digital (4, 75, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(98−69, 98, 208)-Net over F₂₇ — Digital

Digital (29, 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]

(98−69, 98, 6293)-Net in Base 27 — Upper bound on s

There is no (29, 98, 6294)-net in base 27, because

1 times m-reduction [i] would yield (29, 97, 6294)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 6 984428 628801 163623 969516 631837 992576 680086 563777 177870 757945 127172 505563 182907 534936 088260 546306 991090 525536 526367 592218 947567 822370 958285 > 27⁹⁷ [i]