MinT - Best Known (128−45, 128, s)-Nets in Base 5

Best Known (128−45, 128, s)-Nets in Base 5

(128−45, 128, 296)-Net over F₅ — Constructive and digital

Digital (83, 128, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 64, 148)-net over F₂₅, using
- net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
    - a function field by GarcÃa and Quoos [i]

(128−45, 128, 464)-Net over F₅ — Digital

Digital (83, 128, 464)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(128−45, 128, 24517)-Net in Base 5 — Upper bound on s

There is no (83, 128, 24518)-net in base 5, because

1 times m-reduction [i] would yield (83, 127, 24518)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 58810 611153 817716 198720 653143 965473 479159 680736 200627 547679 802087 204237 109329 025078 716225 > 5¹²⁷ [i]