MinT - Best Known (79, 79+33, s)-Nets in Base 4

Best Known (79, 79+33, s)-Nets in Base 4

(79, 79+33, 312)-Net over F₄ — Constructive and digital

Digital (79, 112, 312)-net over F₄, using

2 times m-reduction [i] based on digital (79, 114, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 38, 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]

(79, 79+33, 561)-Net over F₄ — Digital

Digital (79, 112, 561)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(79, 79+33, 34044)-Net in Base 4 — Upper bound on s

There is no (79, 112, 34045)-net in base 4, because

1 times m-reduction [i] would yield (79, 111, 34045)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6 742055 955548 949448 305410 533691 204935 125489 551099 833695 702448 025497 > 4¹¹¹ [i]