MinT - Best Known (98−53, 98, s)-Nets in Base 7

Best Known (98−53, 98, s)-Nets in Base 7

(98−53, 98, 46)-Net over F₇ — Constructive and digital

Digital (45, 98, 46)-net over F₇, using

net from sequence [i] based on digital (45, 45)-sequence over F₇, using
- base reduction for sequences [i] based on digital (0, 45)-sequence over F₄₉, using
  - s-reduction based on digital (0, 49)-sequence over F₄₉, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50, using
      - the rational function field F₄₉(x) [i]
    - Niederreiter sequence [i]

(98−53, 98, 110)-Net over F₇ — Digital

Digital (45, 98, 110)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(98−53, 98, 2483)-Net in Base 7 — Upper bound on s

There is no (45, 98, 2484)-net in base 7, because

1 times m-reduction [i] would yield (45, 97, 2484)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 9470 056573 413540 810618 903708 522311 809302 841516 518033 199480 544131 598751 310088 635705 > 7⁹⁷ [i]