MinT - Best Known (145, 145+43, s)-Nets in Base 4

Best Known (145, 145+43, s)-Nets in Base 4

(145, 145+43, 1044)-Net over F₄ — Constructive and digital

Digital (145, 188, 1044)-net over F₄, using

trace code for nets [i] based on digital (4, 47, 261)-net over F₂₅₆, using
- net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(145, 145+43, 2747)-Net over F₄ — Digital

Digital (145, 188, 2747)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(145, 145+43, 664601)-Net in Base 4 — Upper bound on s

There is no (145, 188, 664602)-net in base 4, because

1 times m-reduction [i] would yield (145, 187, 664602)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 38479 572705 107068 117660 055350 388093 312375 664603 420138 110976 617117 993865 625351 672563 377726 593259 101946 440507 204582 > 4¹⁸⁷ [i]