MinT - Best Known (79, 79+148, s)-Nets in Base 4

Best Known (79, 79+148, s)-Nets in Base 4

(79, 79+148, 104)-Net over F₄ — Constructive and digital

Digital (79, 227, 104)-net over F₄, using

t-expansion [i] based on digital (73, 227, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(79, 79+148, 112)-Net over F₄ — Digital

Digital (79, 227, 112)-net over F₄, using

t-expansion [i] based on digital (73, 227, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(79, 79+148, 605)-Net in Base 4 — Upper bound on s

There is no (79, 227, 606)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 48078 968290 458339 785433 916754 508285 807390 521672 348593 882520 165961 667192 420163 707330 371724 502169 571601 019567 540597 321774 144220 485407 103034 > 4²²⁷ [i]