MinT - Best Known (53, 158, s)-Nets in Base 4

Best Known (53, 158, s)-Nets in Base 4

(53, 158, 66)-Net over F₄ — Constructive and digital

Digital (53, 158, 66)-net over F₄, using

t-expansion [i] based on digital (49, 158, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(53, 158, 91)-Net over F₄ — Digital

Digital (53, 158, 91)-net over F₄, using

t-expansion [i] based on digital (50, 158, 91)-net over F₄, using
- net from sequence [i] based on digital (50, 90)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 50 and N(F) ≥ 91, using
    - a curve from the manYPoints database [i]

(53, 158, 401)-Net in Base 4 — Upper bound on s

There is no (53, 158, 402)-net in base 4, because

1 times m-reduction [i] would yield (53, 157, 402)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 34141 026713 386409 788726 259342 004619 941964 004030 834578 899297 417508 169415 873704 921272 951909 189600 > 4¹⁵⁷ [i]