MinT - Best Known (127−33, 127, s)-Nets in Base 5

Best Known (127−33, 127, s)-Nets in Base 5

(127−33, 127, 408)-Net over F₅ — Constructive and digital

Digital (94, 127, 408)-net over F₅, using

1 times m-reduction [i] based on digital (94, 128, 408)-net over F₅, using
- trace code for nets [i] based on digital (30, 64, 204)-net over F₂₅, using
  - net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
      - a function field by GarcÃa and Quoos [i]

(127−33, 127, 1916)-Net over F₅ — Digital

Digital (94, 127, 1916)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(127−33, 127, 543073)-Net in Base 5 — Upper bound on s

There is no (94, 127, 543074)-net in base 5, because

1 times m-reduction [i] would yield (94, 126, 543074)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 11755 242368 286070 771393 578255 006091 776464 535044 561843 640699 720455 888289 355279 937281 446657 > 5¹²⁶ [i]