MinT - Best Known (139, 139+121, s)-Nets in Base 4

Best Known (139, 139+121, s)-Nets in Base 4

(139, 139+121, 130)-Net over F₄ — Constructive and digital

Digital (139, 260, 130)-net over F₄, using

t-expansion [i] based on digital (105, 260, 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+121, 228)-Net over F₄ — Digital

Digital (139, 260, 228)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(139, 139+121, 3020)-Net in Base 4 — Upper bound on s

There is no (139, 260, 3021)-net in base 4, because

1 times m-reduction [i] would yield (139, 259, 3021)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 865127 105211 430196 162910 852510 840781 261607 600896 133003 227767 027433 972068 070569 962430 264400 582955 785109 702303 051914 468774 240232 751611 013956 835770 938817 699116 > 4²⁵⁹ [i]