MinT - Best Known (98−85, 98, s)-Nets in Base 32

Best Known (98−85, 98, s)-Nets in Base 32

(98−85, 98, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 98, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 98, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(98−85, 98, 129)-Net over F₃₂ — Digital

Digital (13, 98, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 98, 129)-net over F₃₂, using
- net from sequence [i] based on digital (12, 128)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 12 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(98−85, 98, 1572)-Net in Base 32 — Upper bound on s

There is no (13, 98, 1573)-net in base 32, because

1 times m-reduction [i] would yield (13, 97, 1573)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 100 709639 278882 980618 314788 050720 317599 510134 354699 793643 100256 756352 751797 403333 250667 989046 577979 583524 866232 037196 531497 183540 693595 171012 339072 > 32⁹⁷ [i]