MinT - Best Known (98, 98+35, s)-Nets in Base 5

Best Known (98, 98+35, s)-Nets in Base 5

(98, 98+35, 408)-Net over F₅ — Constructive and digital

Digital (98, 133, 408)-net over F₅, using

3 times m-reduction [i] based on digital (98, 136, 408)-net over F₅, using
- trace code for nets [i] based on digital (30, 68, 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]

(98, 98+35, 1852)-Net over F₅ — Digital

Digital (98, 133, 1852)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 98+35, 479921)-Net in Base 5 — Upper bound on s

There is no (98, 133, 479922)-net in base 5, because

1 times m-reduction [i] would yield (98, 132, 479922)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 183 671166 302278 983497 928755 791369 693410 417975 565314 185692 641665 345298 570942 510215 635328 712905 > 5¹³² [i]