MinT - Best Known (98, 98+29, s)-Nets in Base 5

Best Known (98, 98+29, s)-Nets in Base 5

(98, 98+29, 504)-Net over F₅ — Constructive and digital

Digital (98, 127, 504)-net over F₅, using

5¹ times duplication [i] based on digital (97, 126, 504)-net over F₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (34, 48, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 24, 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]
  2. digital (49, 78, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 39, 126)-net over F₂₅, using
      - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(98, 98+29, 4195)-Net over F₅ — Digital

Digital (98, 127, 4195)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 98+29, 2952067)-Net in Base 5 — Upper bound on s

There is no (98, 127, 2952068)-net in base 5, because

1 times m-reduction [i] would yield (98, 126, 2952068)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 11754 959093 308080 301624 411469 161616 899577 512316 037848 256859 347659 274907 734137 392366 119105 > 5¹²⁶ [i]