MinT - Best Known (139, 139+119, s)-Nets in Base 4

Best Known (139, 139+119, s)-Nets in Base 4

(139, 139+119, 130)-Net over F₄ — Constructive and digital

Digital (139, 258, 130)-net over F₄, using

t-expansion [i] based on digital (105, 258, 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]

(139, 139+119, 233)-Net over F₄ — Digital

Digital (139, 258, 233)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(139, 139+119, 3141)-Net in Base 4 — Upper bound on s

There is no (139, 258, 3142)-net in base 4, because

1 times m-reduction [i] would yield (139, 257, 3142)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 54309 346657 190878 574770 535456 312393 157902 641786 367834 418995 968436 111953 242426 062143 311985 589807 771324 329214 173091 249406 727110 555638 621468 905598 699581 826512 > 4²⁵⁷ [i]