MinT - Best Known (147−59, 147, s)-Nets in Base 5

Best Known (147−59, 147, s)-Nets in Base 5

(147−59, 147, 252)-Net over F₅ — Constructive and digital

Digital (88, 147, 252)-net over F₅, using

t-expansion [i] based on digital (85, 147, 252)-net over F₅, using
- 3 times m-reduction [i] based on digital (85, 150, 252)-net over F₅, using
  - trace code for nets [i] based on digital (10, 75, 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]

(147−59, 147, 311)-Net over F₅ — Digital

Digital (88, 147, 311)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−59, 147, 9617)-Net in Base 5 — Upper bound on s

There is no (88, 147, 9618)-net in base 5, because

1 times m-reduction [i] would yield (88, 146, 9618)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 123137 918280 300186 345182 983809 759448 957609 771131 244530 415802 116107 544660 472144 830789 649386 628284 677705 > 5¹⁴⁶ [i]