MinT - Best Known (178−71, 178, s)-Nets in Base 4

Best Known (178−71, 178, s)-Nets in Base 4

(178−71, 178, 130)-Net over F₄ — Constructive and digital

Digital (107, 178, 130)-net over F₄, using

t-expansion [i] based on digital (105, 178, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(178−71, 178, 267)-Net over F₄ — Digital

Digital (107, 178, 267)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−71, 178, 5110)-Net in Base 4 — Upper bound on s

There is no (107, 178, 5111)-net in base 4, because

1 times m-reduction [i] would yield (107, 177, 5111)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 36944 829930 893223 512610 445625 345834 386391 055263 426042 252720 032222 447824 394785 765231 018058 762175 911664 890048 > 4¹⁷⁷ [i]