MinT - Best Known (73, 100, s)-Nets in Base 7

Best Known (73, 100, s)-Nets in Base 7

(73, 100, 688)-Net over F₇ — Constructive and digital

Digital (73, 100, 688)-net over F₇, using

4 times m-reduction [i] based on digital (73, 104, 688)-net over F₇, using
- trace code for nets [i] based on digital (21, 52, 344)-net over F₄₉, using
  - net from sequence [i] based on digital (21, 343)-sequence over F₄₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 21 and N(F) ≥ 344, using
      - the Hermitian function field over F₄₉ [i]

(73, 100, 3143)-Net over F₇ — Digital

Digital (73, 100, 3143)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(73, 100, 2576322)-Net in Base 7 — Upper bound on s

There is no (73, 100, 2576323)-net in base 7, because

1 times m-reduction [i] would yield (73, 99, 2576323)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 462070 107727 456569 036702 085574 422344 701145 937151 377116 102966 206990 367626 686039 021003 > 7⁹⁹ [i]