MinT - Best Known (36, 36+33, s)-Nets in Base 4

Best Known (36, 36+33, s)-Nets in Base 4

(36, 36+33, 56)-Net over F₄ — Constructive and digital

Digital (36, 69, 56)-net over F₄, using

t-expansion [i] based on digital (33, 69, 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]

(36, 36+33, 70)-Net over F₄ — Digital

Digital (36, 69, 70)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(36, 36+33, 807)-Net in Base 4 — Upper bound on s

There is no (36, 69, 808)-net in base 4, because

1 times m-reduction [i] would yield (36, 68, 808)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 87246 028207 800955 563192 068036 896256 918350 > 4⁶⁸ [i]