MinT - Best Known (58, 58+35, s)-Nets in Base 4

Best Known (58, 58+35, s)-Nets in Base 4

(58, 58+35, 130)-Net over F₄ — Constructive and digital

Digital (58, 93, 130)-net over F₄, using

11 times m-reduction [i] based on digital (58, 104, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 52, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(58, 58+35, 190)-Net over F₄ — Digital

Digital (58, 93, 190)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+35, 4321)-Net in Base 4 — Upper bound on s

There is no (58, 93, 4322)-net in base 4, because

1 times m-reduction [i] would yield (58, 92, 4322)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 24 542254 842538 783581 763883 788840 670332 614563 359805 304310 > 4⁹² [i]