MinT - Best Known (107, 153, s)-Nets in Base 4

Best Known (107, 153, s)-Nets in Base 4

(107, 153, 384)-Net over F₄ — Constructive and digital

Digital (107, 153, 384)-net over F₄, using

trace code for nets [i] based on digital (5, 51, 128)-net over F₆₄, using
- net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
    - a function field by SÃ©mirat [i]

(107, 153, 660)-Net over F₄ — Digital

Digital (107, 153, 660)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 153, 31775)-Net in Base 4 — Upper bound on s

There is no (107, 153, 31776)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 130 449210 574528 053922 462085 708807 627682 375380 094947 485796 556054 698850 401250 991965 870979 790059 > 4¹⁵³ [i]