MinT - Best Known (130, 130+59, s)-Nets in Base 4

Best Known (130, 130+59, s)-Nets in Base 4

(130, 130+59, 312)-Net over F₄ — Constructive and digital

Digital (130, 189, 312)-net over F₄, using

t-expansion [i] based on digital (129, 189, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 63, 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]

(130, 130+59, 673)-Net over F₄ — Digital

Digital (130, 189, 673)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(130, 130+59, 31094)-Net in Base 4 — Upper bound on s

There is no (130, 189, 31095)-net in base 4, because

1 times m-reduction [i] would yield (130, 188, 31095)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 154022 157853 756357 283524 670471 049668 484642 822258 915290 422922 292033 492230 744626 116347 055628 645795 134484 953549 278728 > 4¹⁸⁸ [i]