MinT - Best Known (240−59, 240, s)-Nets in Base 4

Best Known (240−59, 240, s)-Nets in Base 4

(240−59, 240, 1032)-Net over F₄ — Constructive and digital

Digital (181, 240, 1032)-net over F₄, using

trace code for nets [i] based on digital (1, 60, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(240−59, 240, 2348)-Net over F₄ — Digital

Digital (181, 240, 2348)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−59, 240, 356267)-Net in Base 4 — Upper bound on s

There is no (181, 240, 356268)-net in base 4, because

1 times m-reduction [i] would yield (181, 239, 356268)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 780444 136766 936553 828578 198343 205484 945364 222039 357392 554642 511094 040426 230459 726089 133532 240664 396945 226321 092035 555962 744839 967344 568267 195064 > 4²³⁹ [i]