MinT - Best Known (39, 39+28, s)-Nets in Base 7

Best Known (39, 39+28, s)-Nets in Base 7

(39, 39+28, 110)-Net over F₇ — Constructive and digital

Digital (39, 67, 110)-net over F₇, using

1 times m-reduction [i] based on digital (39, 68, 110)-net over F₇, using
- trace code for nets [i] based on digital (5, 34, 55)-net over F₄₉, using
  - net from sequence [i] based on digital (5, 54)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(39, 39+28, 232)-Net over F₇ — Digital

Digital (39, 67, 232)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(39, 39+28, 11152)-Net in Base 7 — Upper bound on s

There is no (39, 67, 11153)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 418 798735 261280 740889 208040 347231 694362 115732 522074 891121 > 7⁶⁷ [i]