MinT - Best Known (170−49, 170, s)-Nets in Base 3

Best Known (170−49, 170, s)-Nets in Base 3

(170−49, 170, 246)-Net over F₃ — Constructive and digital

Digital (121, 170, 246)-net over F₃, using

1 times m-reduction [i] based on digital (121, 171, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 57, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(170−49, 170, 440)-Net over F₃ — Digital

Digital (121, 170, 440)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−49, 170, 11198)-Net in Base 3 — Upper bound on s

There is no (121, 170, 11199)-net in base 3, because

1 times m-reduction [i] would yield (121, 169, 11199)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 430 671241 121842 473690 439618 430959 606659 205982 145850 852876 610382 415501 280856 949713 > 3¹⁶⁹ [i]