MinT - Best Known (72, 72+25, s)-Nets in Base 7

Best Known (72, 72+25, s)-Nets in Base 7

(72, 72+25, 688)-Net over F₇ — Constructive and digital

Digital (72, 97, 688)-net over F₇, using

5 times m-reduction [i] based on digital (72, 102, 688)-net over F₇, using
- trace code for nets [i] based on digital (21, 51, 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]

(72, 72+25, 4266)-Net over F₇ — Digital

Digital (72, 97, 4266)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+25, 5081522)-Net in Base 7 — Upper bound on s

There is no (72, 97, 5081523)-net in base 7, because

1 times m-reduction [i] would yield (72, 96, 5081523)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1347 139219 105247 455618 999118 065466 123975 001210 243783 039741 037541 449152 832643 836633 > 7⁹⁶ [i]