MinT - Best Known (131, 131+121, s)-Nets in Base 4

Best Known (131, 131+121, s)-Nets in Base 4

(131, 131+121, 130)-Net over F₄ — Constructive and digital

Digital (131, 252, 130)-net over F₄, using

t-expansion [i] based on digital (105, 252, 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]

(131, 131+121, 200)-Net over F₄ — Digital

Digital (131, 252, 200)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 131+121, 2502)-Net in Base 4 — Upper bound on s

There is no (131, 252, 2503)-net in base 4, because

1 times m-reduction [i] would yield (131, 251, 2503)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 223233 436622 788494 268129 971017 433887 503718 883061 489317 128541 141893 699565 728687 761485 580076 943247 731876 071324 122694 931856 332522 099083 344752 858908 085096 > 4²⁵¹ [i]