MinT - Best Known (98−83, 98, s)-Nets in Base 27

Best Known (98−83, 98, s)-Nets in Base 27

(98−83, 98, 96)-Net over F₂₇ — Constructive and digital

Digital (15, 98, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 98, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(98−83, 98, 136)-Net over F₂₇ — Digital

Digital (15, 98, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 98, 136)-net over F₂₇, using
- net from sequence [i] based on digital (13, 135)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 13 and N(F) ≥ 136, using
    - a curve from the manYPoints database [i]

(98−83, 98, 1489)-Net in Base 27 — Upper bound on s

There is no (15, 98, 1490)-net in base 27, because

1 times m-reduction [i] would yield (15, 97, 1490)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 7 003582 471560 153733 491546 999547 753588 234682 751342 015032 407087 907190 691612 520522 079316 065299 917582 995413 884587 050143 258223 126126 667185 151813 > 27⁹⁷ [i]