MinT - Best Known (17−15, 17, s)-Nets in Base 256

Best Known (17−15, 17, s)-Nets in Base 256

(17−15, 17, 259)-Net over F₂₅₆ — Constructive and digital

Digital (2, 17, 259)-net over F₂₅₆, using

net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(17−15, 17, 321)-Net over F₂₅₆ — Digital

Digital (2, 17, 321)-net over F₂₅₆, using

net from sequence [i] based on digital (2, 320)-sequence over F₂₅₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [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]

(17−15, 17, 4232)-Net in Base 256 — Upper bound on s

There is no (2, 17, 4233)-net in base 256, because

1 times m-reduction [i] would yield (2, 16, 4233)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 340 456581 844967 738019 020086 822328 936056 > 256¹⁶ [i]