MinT - Best Known (217−99, 217, s)-Nets in Base 3

Best Known (217−99, 217, s)-Nets in Base 3

(217−99, 217, 80)-Net over F₃ — Constructive and digital

Digital (118, 217, 80)-net over F₃, using

3 times m-reduction [i] based on digital (118, 220, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 110, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(217−99, 217, 139)-Net over F₃ — Digital

Digital (118, 217, 139)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(217−99, 217, 1164)-Net in Base 3 — Upper bound on s

There is no (118, 217, 1165)-net in base 3, because

1 times m-reduction [i] would yield (118, 216, 1165)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 760517 349140 716036 806022 626415 248810 776722 939770 666364 987231 279847 012029 726781 791460 215193 556386 229595 > 3²¹⁶ [i]