MinT - Best Known (49, 69, s)-Nets in Base 4

Best Known (49, 69, s)-Nets in Base 4

(49, 69, 312)-Net over F₄ — Constructive and digital

Digital (49, 69, 312)-net over F₄, using

trace code for nets [i] based on digital (3, 23, 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]

(49, 69, 415)-Net over F₄ — Digital

Digital (49, 69, 415)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 69, 21523)-Net in Base 4 — Upper bound on s

There is no (49, 69, 21524)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 348545 422511 743562 763375 272343 453106 062586 > 4⁶⁹ [i]