MinT - Best Known (248−113, 248, s)-Nets in Base 4

Best Known (248−113, 248, s)-Nets in Base 4

(248−113, 248, 130)-Net over F₄ — Constructive and digital

Digital (135, 248, 130)-net over F₄, using

t-expansion [i] based on digital (105, 248, 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]

(248−113, 248, 233)-Net over F₄ — Digital

Digital (135, 248, 233)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−113, 248, 3227)-Net in Base 4 — Upper bound on s

There is no (135, 248, 3228)-net in base 4, because

1 times m-reduction [i] would yield (135, 247, 3228)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 51372 425377 433831 832153 241948 456609 456467 546135 796714 226798 961167 194432 615862 977748 876905 937945 906507 397399 241656 585962 893992 218159 096123 409087 642820 > 4²⁴⁷ [i]