MinT - Best Known (64, 64+39, s)-Nets in Base 7

Best Known (64, 64+39, s)-Nets in Base 7

(64, 64+39, 124)-Net over F₇ — Constructive and digital

Digital (64, 103, 124)-net over F₇, using

1 times m-reduction [i] based on digital (64, 104, 124)-net over F₇, using
- trace code for nets [i] based on digital (12, 52, 62)-net over F₄₉, using
  - net from sequence [i] based on digital (12, 61)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(64, 64+39, 501)-Net over F₇ — Digital

Digital (64, 103, 501)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+39, 45476)-Net in Base 7 — Upper bound on s

There is no (64, 103, 45477)-net in base 7, because

1 times m-reduction [i] would yield (64, 102, 45477)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 158 500479 624726 859029 430211 309165 435624 390217 651779 350057 888425 537160 555753 066550 525239 > 7¹⁰² [i]