MinT - Best Known (98, 98+50, s)-Nets in Base 5

Best Known (98, 98+50, s)-Nets in Base 5

(98, 98+50, 296)-Net over F₅ — Constructive and digital

Digital (98, 148, 296)-net over F₅, using

t-expansion [i] based on digital (94, 148, 296)-net over F₅, using
- 2 times m-reduction [i] based on digital (94, 150, 296)-net over F₅, using
  - trace code for nets [i] based on digital (19, 75, 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]

(98, 98+50, 618)-Net over F₅ — Digital

Digital (98, 148, 618)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 98+50, 34933)-Net in Base 5 — Upper bound on s

There is no (98, 148, 34934)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 28 036996 777763 652317 074555 668550 528028 613534 031020 462117 434490 589434 674286 098074 711067 137126 351564 395993 > 5¹⁴⁸ [i]