MinT - Best Known (64, 64+41, s)-Nets in Base 7

Best Known (64, 64+41, s)-Nets in Base 7

(64, 64+41, 122)-Net over F₇ — Constructive and digital

Digital (64, 105, 122)-net over F₇, using

1 times m-reduction [i] based on digital (64, 106, 122)-net over F₇, using
- trace code for nets [i] based on digital (11, 53, 61)-net over F₄₉, using
  - net from sequence [i] based on digital (11, 60)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(64, 64+41, 439)-Net over F₇ — Digital

Digital (64, 105, 439)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+41, 34316)-Net in Base 7 — Upper bound on s

There is no (64, 105, 34317)-net in base 7, because

1 times m-reduction [i] would yield (64, 104, 34317)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 7768 441432 192730 681547 346787 977042 261933 182803 073086 692807 386704 448994 598053 309383 379297 > 7¹⁰⁴ [i]