MinT - Best Known (14, 14+22, s)-Nets in Base 256

Best Known (14, 14+22, s)-Nets in Base 256

(14, 14+22, 517)-Net over F₂₅₆ — Constructive and digital

Digital (14, 36, 517)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (1, 12, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]
2. digital (2, 24, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(14, 14+22, 610)-Net over F₂₅₆ — Digital

Digital (14, 36, 610)-net over F₂₅₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(256³⁶, 610, F₂₅₆, 2, 22) (dual of [(610, 2), 1184, 23]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256¹², 289, F₂₅₆, 2, 11) (dual of [(289, 2), 566, 12]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,566P) [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
      - sharp bound on the number of rational points on curves with genus 1 [i]
  2. linear OOA(256²⁴, 321, F₂₅₆, 2, 22) (dual of [(321, 2), 618, 23]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,619P) [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
      - sharp bound on the number of rational points on curves with genus 2 [i]

(14, 14+22, 1465497)-Net in Base 256 — Upper bound on s

There is no (14, 36, 1465498)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 497 324938 112065 657084 349088 576222 401210 901455 329060 845895 244988 160735 944906 755808 267016 > 256³⁶ [i]