MinT - Best Known (103−27, 103, s)-Nets in Base 7

Best Known (103−27, 103, s)-Nets in Base 7

(103−27, 103, 688)-Net over F₇ — Constructive and digital

Digital (76, 103, 688)-net over F₇, using

7 times m-reduction [i] based on digital (76, 110, 688)-net over F₇, using
- trace code for nets [i] based on digital (21, 55, 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]

(103−27, 103, 3931)-Net over F₇ — Digital

Digital (76, 103, 3931)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(103−27, 103, 4036670)-Net in Base 7 — Upper bound on s

There is no (76, 103, 4036671)-net in base 7, because

1 times m-reduction [i] would yield (76, 102, 4036671)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 158 489673 605878 580951 001154 562659 443488 518963 651153 726988 045348 317300 836629 468079 715123 > 7¹⁰² [i]