MinT - Best Known (129, 228, s)-Nets in Base 4

Best Known (129, 228, s)-Nets in Base 4

(129, 228, 130)-Net over F₄ — Constructive and digital

Digital (129, 228, 130)-net over F₄, using

t-expansion [i] based on digital (105, 228, 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]

(129, 228, 252)-Net over F₄ — Digital

Digital (129, 228, 252)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(129, 228, 3880)-Net in Base 4 — Upper bound on s

There is no (129, 228, 3881)-net in base 4, because

1 times m-reduction [i] would yield (129, 227, 3881)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47014 725092 341332 250567 133395 719832 062741 196598 729744 786199 562059 815738 178275 334283 055436 674513 485326 023992 241426 718897 165129 234686 639296 > 4²²⁷ [i]