MinT - Best Known (122−60, 122, s)-Nets in Base 9

Best Known (122−60, 122, s)-Nets in Base 9

(122−60, 122, 200)-Net over F₉ — Constructive and digital

Digital (62, 122, 200)-net over F₉, using

trace code for nets [i] based on digital (1, 61, 100)-net over F₈₁, using
- net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]

(122−60, 122, 250)-Net over F₉ — Digital

Digital (62, 122, 250)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(122−60, 122, 11418)-Net in Base 9 — Upper bound on s

There is no (62, 122, 11419)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 262 227444 877624 530274 460664 907771 452117 552047 714266 495749 141021 079016 050080 651069 938143 127677 222612 201520 395735 995601 > 9¹²² [i]