MinT - Best Known (105−37, 105, s)-Nets in Base 7

Best Known (105−37, 105, s)-Nets in Base 7

(105−37, 105, 130)-Net over F₇ — Constructive and digital

Digital (68, 105, 130)-net over F₇, using

1 times m-reduction [i] based on digital (68, 106, 130)-net over F₇, using
- trace code for nets [i] based on digital (15, 53, 65)-net over F₄₉, using
  - net from sequence [i] based on digital (15, 64)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(105−37, 105, 712)-Net over F₇ — Digital

Digital (68, 105, 712)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−37, 105, 96098)-Net in Base 7 — Upper bound on s

There is no (68, 105, 96099)-net in base 7, because

1 times m-reduction [i] would yield (68, 104, 96099)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 7767 057298 371016 336049 026081 444223 519217 092484 310431 662752 853352 756627 027340 898217 331933 > 7¹⁰⁴ [i]