MinT - Best Known (98−81, 98, s)-Nets in Base 27

Best Known (98−81, 98, s)-Nets in Base 27

(98−81, 98, 96)-Net over F₂₇ — Constructive and digital

Digital (17, 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]

(98−81, 98, 144)-Net over F₂₇ — Digital

Digital (17, 98, 144)-net over F₂₇, using

t-expansion [i] based on digital (16, 98, 144)-net over F₂₇, using
- net from sequence [i] based on digital (16, 143)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 16 and N(F) ≥ 144, using
    - a curve from the manYPoints database [i]

(98−81, 98, 1773)-Net in Base 27 — Upper bound on s

There is no (17, 98, 1774)-net in base 27, because

1 times m-reduction [i] would yield (17, 97, 1774)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 7 074785 365675 882806 025335 153354 014570 910167 823862 483804 355584 343418 327712 448860 102067 025059 010562 237871 555115 119398 711914 968595 068027 904657 > 27⁹⁷ [i]