MinT - Best Known (21, 76, s)-Nets in Base 4

Best Known (21, 76, s)-Nets in Base 4

(21, 76, 34)-Net over F₄ — Constructive and digital

Digital (21, 76, 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]

(21, 76, 44)-Net over F₄ — Digital

Digital (21, 76, 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]

(21, 76, 99)-Net in Base 4 — Upper bound on s

There is no (21, 76, 100)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁷⁶, 100, S₄, 55), but
- the linear programming bound shows that MÂ â‰¥ 261 756261 823685 636851 226557 955451 557478 297379 280525 495829 004288 / 41746 366485 659563 > 4⁷⁶ [i]