MinT - Best Known (33, 77, s)-Nets in Base 4

Best Known (33, 77, s)-Nets in Base 4

(33, 77, 56)-Net over F₄ — Constructive and digital

Digital (33, 77, 56)-net over F₄, using

net from sequence [i] based on digital (33, 55)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
  - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(33, 77, 65)-Net over F₄ — Digital

Digital (33, 77, 65)-net over F₄, using

net from sequence [i] based on digital (33, 64)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 65, using
  - Drinfeld modules of rank 1 [i]

(33, 77, 368)-Net in Base 4 — Upper bound on s

There is no (33, 77, 369)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 23107 767322 915172 867270 627830 061805 336692 258320 > 4⁷⁷ [i]