MinT - Best Known (119−57, 119, s)-Nets in Base 4

Best Known (119−57, 119, s)-Nets in Base 4

(119−57, 119, 66)-Net over F₄ — Constructive and digital

Digital (62, 119, 66)-net over F₄, using

t-expansion [i] based on digital (49, 119, 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]

(119−57, 119, 106)-Net over F₄ — Digital

Digital (62, 119, 106)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(119−57, 119, 1274)-Net in Base 4 — Upper bound on s

There is no (62, 119, 1275)-net in base 4, because

1 times m-reduction [i] would yield (62, 118, 1275)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 110649 336883 310084 028360 393632 703583 396651 479048 280953 607081 429473 980344 > 4¹¹⁸ [i]