MinT - Best Known (135−41, 135, s)-Nets in Base 4

Best Known (135−41, 135, s)-Nets in Base 4

(135−41, 135, 312)-Net over F₄ — Constructive and digital

Digital (94, 135, 312)-net over F₄, using

t-expansion [i] based on digital (93, 135, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 45, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(135−41, 135, 574)-Net over F₄ — Digital

Digital (94, 135, 574)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−41, 135, 29905)-Net in Base 4 — Upper bound on s

There is no (94, 135, 29906)-net in base 4, because

1 times m-reduction [i] would yield (94, 134, 29906)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 474 417007 667432 606544 260960 657748 433540 051953 536981 219839 239724 147282 029656 688784 > 4¹³⁴ [i]