MinT - Best Known (139, 139+115, s)-Nets in Base 4

Best Known (139, 139+115, s)-Nets in Base 4

(139, 139+115, 130)-Net over F₄ — Constructive and digital

Digital (139, 254, 130)-net over F₄, using

t-expansion [i] based on digital (105, 254, 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+115, 243)-Net over F₄ — Digital

Digital (139, 254, 243)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(139, 139+115, 3414)-Net in Base 4 — Upper bound on s

There is no (139, 254, 3415)-net in base 4, because

1 times m-reduction [i] would yield (139, 253, 3415)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 212 852400 143358 269690 127377 169701 062018 842936 065301 224712 882172 294045 996529 011512 968360 537675 583598 685993 053922 864132 494974 597822 093878 307272 796974 896720 > 4²⁵³ [i]