MinT - Best Known (66−36, 66, s)-Nets in Base 7

Best Known (66−36, 66, s)-Nets in Base 7

(66−36, 66, 33)-Net over F₇ — Constructive and digital

Digital (30, 66, 33)-net over F₇, using

t-expansion [i] based on digital (29, 66, 33)-net over F₇, using
- net from sequence [i] based on digital (29, 32)-sequence over F₇, using
  - Niederreiter sequence [i]

(66−36, 66, 79)-Net over F₇ — Digital

Digital (30, 66, 79)-net over F₇, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(7⁶⁶, 79, F₇, 3, 36) (dual of [(79, 3), 171, 37]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(7⁶³, 78, F₇, 3, 36) (dual of [(78, 3), 171, 37]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,197P) [i] based on function field F/F₇ with g(F) = 27 and N(F) ≥ 78, using
    - an algebraic function field by Teo [i]

(66−36, 66, 1568)-Net in Base 7 — Upper bound on s

There is no (30, 66, 1569)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 60 054794 383088 437720 450861 040012 146462 734680 688044 322289 > 7⁶⁶ [i]