MinT - Best Known (22, 77, s)-Nets in Base 4

Best Known (22, 77, s)-Nets in Base 4

(22, 77, 34)-Net over F₄ — Constructive and digital

Digital (22, 77, 34)-net over F₄, using

t-expansion [i] based on digital (21, 77, 34)-net over F₄, using
- net from sequence [i] based on digital (21, 33)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
    - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(22, 77, 44)-Net over F₄ — Digital

Digital (22, 77, 44)-net over F₄, using

t-expansion [i] based on digital (21, 77, 44)-net over F₄, using
- net from sequence [i] based on digital (21, 43)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 44, using
    - a curve from the manYPoints database [i]

(22, 77, 110)-Net in Base 4 — Upper bound on s

There is no (22, 77, 111)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁷⁷, 111, S₄, 55), but
- the linear programming bound shows that MÂ â‰¥ 5 888442 347878 486849 802070 789382 718733 257438 621543 296434 852235 010474 246144 / 236 608175 959111 292935 306575 > 4⁷⁷ [i]