MinT - Best Known (95−68, 95, s)-Nets in Base 27

Best Known (95−68, 95, s)-Nets in Base 27

(95−68, 95, 114)-Net over F₂₇ — Constructive and digital

Digital (27, 95, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 95, 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]

(95−68, 95, 116)-Net in Base 27 — Constructive

(27, 95, 116)-net in base 27, using

5 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]

(95−68, 95, 208)-Net over F₂₇ — Digital

Digital (27, 95, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 95, 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]

(95−68, 95, 5180)-Net in Base 27 — Upper bound on s

There is no (27, 95, 5181)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 9541 536530 927849 309275 142343 202520 259517 055270 309307 806580 520834 663820 372896 223558 558326 863806 682355 560178 371788 406639 152414 953497 098577 > 27⁹⁵ [i]