MinT - Best Known (66, 66+39, s)-Nets in Base 7

Best Known (66, 66+39, s)-Nets in Base 7

(66, 66+39, 126)-Net over F₇ — Constructive and digital

Digital (66, 105, 126)-net over F₇, using

1 times m-reduction [i] based on digital (66, 106, 126)-net over F₇, using
- trace code for nets [i] based on digital (13, 53, 63)-net over F₄₉, using
  - net from sequence [i] based on digital (13, 62)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(66, 66+39, 559)-Net over F₇ — Digital

Digital (66, 105, 559)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+39, 55817)-Net in Base 7 — Upper bound on s

There is no (66, 105, 55818)-net in base 7, because

1 times m-reduction [i] would yield (66, 104, 55818)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 7767 630718 686858 294916 194915 458397 732529 956829 680749 756748 200384 911596 728818 030537 165417 > 7¹⁰⁴ [i]