MinT - Best Known (130−47, 130, s)-Nets in Base 5

Best Known (130−47, 130, s)-Nets in Base 5

(130−47, 130, 252)-Net over F₅ — Constructive and digital

Digital (83, 130, 252)-net over F₅, using

16 times m-reduction [i] based on digital (83, 146, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 73, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(130−47, 130, 418)-Net over F₅ — Digital

Digital (83, 130, 418)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−47, 130, 19603)-Net in Base 5 — Upper bound on s

There is no (83, 130, 19604)-net in base 5, because

1 times m-reduction [i] would yield (83, 129, 19604)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 470082 296116 336820 185021 380514 441933 252211 347871 035765 536830 346743 988587 499855 054046 449105 > 5¹²⁹ [i]