MinT - Best Known (64, 64+37, s)-Nets in Base 7

Best Known (64, 64+37, s)-Nets in Base 7

(64, 64+37, 126)-Net over F₇ — Constructive and digital

Digital (64, 101, 126)-net over F₇, using

1 times m-reduction [i] based on digital (64, 102, 126)-net over F₇, using
- trace code for nets [i] based on digital (13, 51, 63)-net over F₄₉, using
  - net from sequence [i] based on digital (13, 62)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(64, 64+37, 577)-Net over F₇ — Digital

Digital (64, 101, 577)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+37, 62357)-Net in Base 7 — Upper bound on s

There is no (64, 101, 62358)-net in base 7, because

1 times m-reduction [i] would yield (64, 100, 62358)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 3 235058 390132 720026 260270 350107 110263 954625 811934 980160 385798 580111 364428 699257 506365 > 7¹⁰⁰ [i]