MinT - Best Known (78, 78+34, s)-Nets in Base 4

Best Known (78, 78+34, s)-Nets in Base 4

(78, 78+34, 312)-Net over F₄ — Constructive and digital

Digital (78, 112, 312)-net over F₄, using

4¹ times duplication [i] based on digital (77, 111, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 37, 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]

(78, 78+34, 500)-Net over F₄ — Digital

Digital (78, 112, 500)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+34, 22134)-Net in Base 4 — Upper bound on s

There is no (78, 112, 22135)-net in base 4, because

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]