MinT - Best Known (76−36, 76, s)-Nets in Base 7

Best Known (76−36, 76, s)-Nets in Base 7

(76−36, 76, 104)-Net over F₇ — Constructive and digital

Digital (40, 76, 104)-net over F₇, using

trace code for nets [i] based on digital (2, 38, 52)-net over F₄₉, using
- net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
  - Niederreiter sequence [i]

(76−36, 76, 156)-Net over F₇ — Digital

Digital (40, 76, 156)-net over F₇, using

trace code for nets [i] based on digital (2, 38, 78)-net over F₄₉, using
- net from sequence [i] based on digital (2, 77)-sequence over F₄₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 2 and N(F) ≥ 78, using
    - sharp bound on the number of rational points on curves with genus 2 [i]

(76−36, 76, 4646)-Net in Base 7 — Upper bound on s

There is no (40, 76, 4647)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 16935 410786 300749 198585 799313 006828 960812 922568 349999 559476 606245 > 7⁷⁶ [i]