MinT - Best Known (58−28, 58, s)-Nets in Base 7

Best Known (58−28, 58, s)-Nets in Base 7

(58−28, 58, 102)-Net over F₇ — Constructive and digital

Digital (30, 58, 102)-net over F₇, using

trace code for nets [i] based on digital (1, 29, 51)-net over F₄₉, using
- net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
  - Niederreiter sequence [i]

(58−28, 58, 128)-Net over F₇ — Digital

Digital (30, 58, 128)-net over F₇, using

trace code for nets [i] based on digital (1, 29, 64)-net over F₄₉, using
- net from sequence [i] based on digital (1, 63)-sequence over F₄₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 1 and N(F) ≥ 64, using
    - sharp bound on the number of rational points on curves with genus 1 [i]

(58−28, 58, 3185)-Net in Base 7 — Upper bound on s

There is no (30, 58, 3186)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 10 374536 156203 650239 546777 359299 561751 038047 269693 > 7⁵⁸ [i]