MinT - Best Known (78, 78+35, s)-Nets in Base 4

Best Known (78, 78+35, s)-Nets in Base 4

(78, 78+35, 240)-Net over F₄ — Constructive and digital

Digital (78, 113, 240)-net over F₄, using

t-expansion [i] based on digital (77, 113, 240)-net over F₄, using
- 1 times m-reduction [i] based on digital (77, 114, 240)-net over F₄, using
  - trace code for nets [i] based on digital (1, 38, 80)-net over F₆₄, using
    - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
        a function field by SÃ©mirat [i]

(78, 78+35, 462)-Net over F₄ — Digital

Digital (78, 113, 462)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+35, 22134)-Net in Base 4 — Upper bound on s

There is no (78, 113, 22135)-net in base 4, because

1 times m-reduction [i] would yield (78, 112, 22135)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 26 971227 141159 531668 382713 937136 678376 662678 967975 168492 075500 958458 > 4¹¹² [i]