MinT - Best Known (98, 98+41, s)-Nets in Base 8

Best Known (98, 98+41, s)-Nets in Base 8

(98, 98+41, 1026)-Net over F₈ — Constructive and digital

Digital (98, 139, 1026)-net over F₈, using

1 times m-reduction [i] based on digital (98, 140, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 70, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(98, 98+41, 3117)-Net over F₈ — Digital

Digital (98, 139, 3117)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 98+41, 2020814)-Net in Base 8 — Upper bound on s

There is no (98, 139, 2020815)-net in base 8, because

1 times m-reduction [i] would yield (98, 138, 2020815)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 42307 799193 644993 656512 322027 564436 965763 343161 521273 628554 530396 557893 663134 694399 964296 734659 746987 233831 601611 360991 581724 > 8¹³⁸ [i]